11 results on '"Geometric function theory"'
Search Results
2. On a geometric study of a class of normalized functions defined by Bernoulli's formula.
- Author
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Ibrahim, Rabha W., Aldawish, Ibtisam, and Baleanu, Dumitru
- Subjects
- *
UNIVALENT functions , *HYPERGEOMETRIC functions , *STAR-like functions , *SPECIAL functions , *ANALYTIC functions , *GEOMETRIC function theory - Abstract
The central purpose of this effort is to investigate analytic and geometric properties of a class of normalized analytic functions in the open unit disk involving Bernoulli's formula. As a consequence, some solutions are indicated by the well-known hypergeometric function. The class of starlike functions is investigated containing the suggested class. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
3. On a new linear operator formulated by Airy functions in the open unit disk.
- Author
-
Ibrahim, Rabha W. and Baleanu, Dumitru
- Subjects
- *
AIRY functions , *GEOMETRIC function theory , *UNIVALENT functions , *ANALYTIC functions , *LINEAR operators - Abstract
In this note, we formulate a new linear operator given by Airy functions of the first type in a complex domain. We aim to study the operator in view of geometric function theory based on the subordination and superordination concepts. The new operator is suggested to define a class of normalized functions (the class of univalent functions) calling the Airy difference formula. As a result, the suggested difference formula joining the linear operator is modified to different classes of analytic functions in the open unit disk. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
4. On subclasses of analytic functions based on a quantum symmetric conformable differential operator with application.
- Author
-
Ibrahim, Rabha W., Elobaid, Rafida M., and Obaiys, Suzan J.
- Subjects
- *
DIFFERENTIAL operators , *ANALYTIC functions , *GEOMETRIC function theory , *DIFFERENTIAL equations , *FLUID mechanics , *CALCULUS , *COMBINATORICS - Abstract
Quantum calculus (the calculus without limit) appeared for the first time in fluid mechanics, noncommutative geometry and combinatorics studies. Recently, it has been included into the field of geometric function theory to extend differential operators, integral operators, and classes of analytic functions, especially the classes that are generated by convolution product (Hadamard product). In this effort, we aim to introduce a quantum symmetric conformable differential operator (Q-SCDO). This operator generalized some well-know differential operators such as Sàlàgean differential operator. By employing the Q-SCDO, we present subclasses of analytic functions to study some of its geometric solutions of q-Painlevé differential equation (type III). [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
5. On a new linear operator formulated by Airy functions in the open unit disk
- Author
-
Dumitru Baleanu and Rabha W. Ibrahim
- Subjects
Pure mathematics ,Algebra and Number Theory ,Partial differential equation ,Geometric function theory ,Applied Mathematics ,Univalent function ,Subordination ,01 natural sciences ,Unit disk ,Domain (mathematical analysis) ,010305 fluids & plasmas ,Linear map ,Operator (computer programming) ,Analytic function ,Airy function ,Open unit disk ,0103 physical sciences ,QA1-939 ,010306 general physics ,Analysis ,Mathematics - Abstract
In this note, we formulate a new linear operator given by Airy functions of the first type in a complex domain. We aim to study the operator in view of geometric function theory based on the subordination and superordination concepts. The new operator is suggested to define a class of normalized functions (the class of univalent functions) calling the Airy difference formula. As a result, the suggested difference formula joining the linear operator is modified to different classes of analytic functions in the open unit disk.
- Published
- 2021
6. Analytic Solution of the Langevin Differential Equations Dominated by a Multibrot Fractal Set
- Author
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Rabha W. Ibrahim and Dumitru Baleanu
- Subjects
Statistics and Probability ,Geometric function theory ,Differential equation ,Boundary (topology) ,010103 numerical & computational mathematics ,fractional calculus ,univalent function ,01 natural sciences ,Computer Science::Digital Libraries ,Domain (mathematical analysis) ,analytic function ,fractional differential operator ,Fractal ,QA1-939 ,0101 mathematics ,complex fractal domain ,open unit disk ,Mathematics ,QA299.6-433 ,Mathematical analysis ,Statistical and Nonlinear Physics ,Function (mathematics) ,010101 applied mathematics ,Thermodynamics ,subordination and superordination ,QC310.15-319 ,Analysis ,algebraic differential equations ,Analytic function ,Univalent function - Abstract
We present an analytic solvability of a class of Langevin differential equations (LDEs) in the asset of geometric function theory. The analytic solutions of the LDEs are presented by utilizing a special kind of fractal function in a complex domain, linked with the subordination theory. The fractal functions are suggested for the multi-parametric coefficients type motorboat fractal set. We obtain different formulas of fractal analytic solutions of LDEs. Moreover, we determine the maximum value of the fractal coefficients to obtain the optimal solution. Through the subordination inequality, we determined the upper boundary determination of a class of fractal functions holding multibrot function ϑ(z)=1+3κz+z3.
- Published
- 2021
- Full Text
- View/download PDF
7. On subclasses of analytic functions based on a quantum symmetric conformable differential operator with application
- Author
-
Rabha W. Ibrahim, Suzan Jabbar Obaiys, and Rafida M. Elobaid
- Subjects
Subordination and superordination ,Pure mathematics ,Algebra and Number Theory ,Partial differential equation ,Geometric function theory ,Differential equation ,lcsh:Mathematics ,Applied Mathematics ,Univalent function ,Conformable fractional derivative ,Quantum calculus ,lcsh:QA1-939 ,Differential operator ,Analytic function ,Operator (computer programming) ,Open unit disk ,Ordinary differential equation ,Analysis ,Mathematics - Abstract
Quantum calculus (the calculus without limit) appeared for the first time in fluid mechanics, noncommutative geometry and combinatorics studies. Recently, it has been included into the field of geometric function theory to extend differential operators, integral operators, and classes of analytic functions, especially the classes that are generated by convolution product (Hadamard product). In this effort, we aim to introduce a quantum symmetric conformable differential operator (Q-SCDO). This operator generalized some well-know differential operators such as Sàlàgean differential operator. By employing the Q-SCDO, we present subclasses of analytic functions to study some of its geometric solutions of q-Painlevé differential equation (type III).
- Published
- 2020
8. On the Connection Problem for Painlevé Differential Equation in View of Geometric Function Theory
- Author
-
Suzan Jabbar Obaiys, Rafida M. Elobaid, and Rabha W. Ibrahim
- Subjects
Asymptotic analysis ,Geometric function theory ,Differential equation ,General Mathematics ,univalent function ,01 natural sciences ,Domain (mathematical analysis) ,analytic function ,Painlevé differential equation ,Computer Science (miscellaneous) ,Applied mathematics ,0101 mathematics ,Engineering (miscellaneous) ,Mathematics ,asymptotic expansion ,lcsh:Mathematics ,010102 general mathematics ,Function (mathematics) ,lcsh:QA1-939 ,open unit disk ,Connection (mathematics) ,010101 applied mathematics ,symmetric solution ,subordination and superordination ,Asymptotic expansion ,Univalent function - Abstract
Asymptotic analysis is a branch of mathematical analysis that describes the limiting behavior of the function. This behavior appears when we study the solution of differential equations analytically. The recent work deals with a special class of third type of Painlevé, differential equation (PV). Our aim is to find asymptotic, symmetric univalent solution of this class in a symmetric domain with respect to the real axis. As a result that the most important problem in the asymptotic expansion is the connections bound (coefficients bound), we introduce a study of this problem.
- Published
- 2020
9. Symmetric Conformable Fractional Derivative of Complex Variables
- Author
-
Rabha W. Ibrahim, Rafida M. Elobaid, and Suzan Jabbar Obaiys
- Subjects
0209 industrial biotechnology ,Pure mathematics ,Geometric function theory ,Differential equation ,General Mathematics ,02 engineering and technology ,univalent function ,01 natural sciences ,analytic function ,Convexity ,020901 industrial engineering & automation ,Computer Science (miscellaneous) ,0101 mathematics ,Engineering (miscellaneous) ,open unit disk ,Mathematics ,conformable fractional derivative ,lcsh:Mathematics ,lcsh:QA1-939 ,Differential operator ,Unit disk ,Fractional calculus ,010101 applied mathematics ,subordination and superordination ,Analytic function ,Univalent function - Abstract
It is well known that the conformable and the symmetric differential operators have formulas in terms of the first derivative. In this document, we combine the two definitions to get the symmetric conformable derivative operator (SCDO). The purpose of this effort is to provide a study of SCDO connected with the geometric function theory. These differential operators indicate a generalization of well known differential operator including the Sà, là, gean differential operator. Our contribution is to impose two classes of symmetric differential operators in the open unit disk and to describe the further development of these operators by introducing convex linear symmetric operators. In addition, by acting these SCDOs on the class of univalent functions, we display a set of sub-classes of analytic functions having geometric representation, such as starlikeness and convexity properties. Investigations in this direction lead to some applications in the univalent function theory of well known formulas, by defining and studying some sub-classes of analytic functions type Janowski function and convolution structures. Moreover, by using the SCDO, we introduce a generalized class of Briot&ndash, Bouquet differential equations to introduce, what is called the symmetric conformable Briot&ndash, Bouquet differential equations. We shall show that the upper bound of this class is symmetric in the open unit disk.
- Published
- 2020
10. On the Connection Problem for Painlevé Differential Equation in View of Geometric Function Theory.
- Author
-
Ibrahim, Rabha W., Elobaid, Rafida M., and Obaiys, Suzan J.
- Subjects
- *
PAINLEVE equations , *DIFFERENTIAL equations , *SYMMETRIC domains , *GEOMETRIC function theory , *MATHEMATICAL analysis , *ANALYTIC functions - Abstract
Asymptotic analysis is a branch of mathematical analysis that describes the limiting behavior of the function. This behavior appears when we study the solution of differential equations analytically. The recent work deals with a special class of third type of Painlevé differential equation (PV). Our aim is to find asymptotic, symmetric univalent solution of this class in a symmetric domain with respect to the real axis. As a result that the most important problem in the asymptotic expansion is the connections bound (coefficients bound), we introduce a study of this problem. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
11. Symmetric Conformable Fractional Derivative of Complex Variables.
- Author
-
Ibrahim, Rabha W., Elobaid, Rafida M., and Obaiys, Suzan J.
- Subjects
- *
SYMMETRIC operators , *COMPLEX variables , *DIFFERENTIAL operators , *DIFFERENTIAL equations , *ANALYTIC functions , *LINEAR operators , *STAR-like functions , *GEOMETRIC function theory - Abstract
It is well known that the conformable and the symmetric differential operators have formulas in terms of the first derivative. In this document, we combine the two definitions to get the symmetric conformable derivative operator (SCDO). The purpose of this effort is to provide a study of SCDO connected with the geometric function theory. These differential operators indicate a generalization of well known differential operator including the Sàlàgean differential operator. Our contribution is to impose two classes of symmetric differential operators in the open unit disk and to describe the further development of these operators by introducing convex linear symmetric operators. In addition, by acting these SCDOs on the class of univalent functions, we display a set of sub-classes of analytic functions having geometric representation, such as starlikeness and convexity properties. Investigations in this direction lead to some applications in the univalent function theory of well known formulas, by defining and studying some sub-classes of analytic functions type Janowski function and convolution structures. Moreover, by using the SCDO, we introduce a generalized class of Briot–Bouquet differential equations to introduce, what is called the symmetric conformable Briot–Bouquet differential equations. We shall show that the upper bound of this class is symmetric in the open unit disk. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
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